Radial Basis Functions with Partition of Unity Method for American Options with Stochastic Volatility

In this article, we price American options under Heston’s stochastic volatility model using a radial basis function (RBF) with partition of unity method (PUM) applied to a linear complementary formulation of the free boundary partial differential equation problem. RBF-PUMs are local meshfree methods...

Full description

Saved in:
Bibliographic Details
Published in:Computational economics 2019-01, Vol.53 (1), p.259-287
Main Authors: Mollapourasl, Reza, Fereshtian, Ali, Vanmaele, Michèle
Format: Article
Language:English
Subjects:
Accuracy
Basis functions
Behavioral/Experimental Economics
Computer Appl. in Social and Behavioral Sciences
Discretization
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Free boundaries
Geometry
Math Applications in Computer Science
Mathematical analysis
Mathematical models
Matrices
Meshless methods
Operations Research/Decision Theory
Operators (mathematics)
Options trading
Partial differential equations
Partition
Partitions
Radial basis function
Sparse matrices
Unity
Volatility
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this article, we price American options under Heston’s stochastic volatility model using a radial basis function (RBF) with partition of unity method (PUM) applied to a linear complementary formulation of the free boundary partial differential equation problem. RBF-PUMs are local meshfree methods that are accurate and flexible with respect to the problem geometry and that produce algebraic problems with sparse matrices which have a moderate condition number. Next, a Crank–Nicolson time discretisation is combined with the operator splitting method to get a fully discrete problem. To better control the computational cost and the accuracy, adaptivity is used in the spatial discretisation. Numerical experiments illustrate the accuracy and efficiency of the proposed algorithm.
ISSN:0927-7099
1572-9974
DOI:10.1007/s10614-017-9739-8